Biomedical Engineering Reference
In-Depth Information
10.6.1
Optimal Geometry for Tangential Interfacial Displacement -
f
d
Numerical results for the minimization of relative tangential displacement objective
function are presented in Table 10.2. For the initial shape, half coated stems have
greater function values than totally coated ones. For optimized shapes, totally
coated implants also present lower
f
d
values. In Table 10.2 it is also possible to
verify a reduction of approximately 50% in objective function values.
In Figure 10.10, it is possible to compare the optimized shapes with the initial
solution. Section 2 (see section numbers in Figure 10.10) is rectangular (parameter
p
) and is larger (parameter
a
) than the initial one, improving rotational stability.
It is also possible to observe a small section 1, which is big enough for a slight
fixation on cortical bone. These two sections, 1 and 2, define a distal wedge design,
important to improve axial stability. Section 3 is also larger to increase cortical
fixation at elbow region (see Figure 10.1). Finally, section 4 is thinner (parameter
b
) and almost rectangular to improve rotational stability.
Although the characteristics mentioned above are similar for half and totally
coated stems, there are some details that depend on coating length. For instance,
for half coated stems section 2 and 3 are thin (parameter
b
) and the distal tip is
larger (parameter
a
) than for the totally coated stems, to compensate the lack of
friction in the distal part.
In Figure 10.11 it can be observed that the area with tangential displacements
below 25
m increases from the initial to the optimized shapes. Furthermore, for
optimized geometries, displacements greater than 50
µ
µ
m are concentrated in small
Table 10.2
Objective function values. Minimization of displacement function
f
d
.
f
d
−
initial
f
d
−
final
Totally coated
40.18
21.58
Half coated
52.41
26.98
4
3
Optimized
Totally
coated
Optimized
Half
coated
Initial
2
1
Figure 10.10
Initial and optimized stems. Minimization of displacement function
f
d
.
